A229627 a(n) is the smallest prime q such that 2*q^k - 1 is prime for k = 1, 2, ..., n.

2, 2, 3, 92581, 385939, 464938699, 24137752519, 1095265755949

Offset: 1

Author

Farideh Firoozbakht, Sep 27 2013

Keywords

• nonn
• more

Comments

The prime number 2 in the definition is used because 2 is the only prime p such that p*q^k - 1 can be prime for more than one prime q.

a(9) > 3*10^13. - Tyler Busby, Jan 14 2023

Crossrefs

Cf. A005382, A106483, A177104, A182785, A309855, A229626.

Programs

Mathematica

a[1]=2;a[n_]:=a[n]=(For[m=PrimePi[a[n-1]],Union[Table[PrimeQ[2 Prime[m]^k-1],{k,n}]]!={True},m++];Prime[m])

PARI

a(n)=forprime(m=2,,for(k=1,n,if(!ispseudoprime(2*m^k-1), next(2))); return(m)) \\ Charles R Greathouse IV, Oct 01 2013

Extensions

a(7) from Giovanni Resta, Oct 01 2013

a(8) from Tyler Busby, Jan 06 2023